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          <title>scalation.math.MatrixN</title>
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        <p id="owner"><a name="scalation" class="extype" href="../package.html">scalation</a>.<a name="scalation.math" class="extype" href="package.html">math</a></p>
        <h1>MatrixN</h1>
      </div>

      <h4 class="signature" id="signature">
      <span class="kind">class</span>
      <span class="symbol"> 
        <span class="name">MatrixN</span>
        <span class="tparams">[<span name="T">T</span>]</span>
        <span class="result"> extends <a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a>[T] with <a name="scalation.util.Error" class="extype" href="../util/Error.html">Error</a></span>
      </span>
      </h4>
      
          <div class="fullcommenttop" id="comment"><div class="comment cmt"><p>:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
The MatrixN class stores and operates on Numeric Matrices of various sizes
and types.  The element type may be any subtype of Numeric.</p></div><div class="toggleContainer block">
          <span class="toggle">Linear Supertypes</span>
          <div class="superTypes hiddenContent"><a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a>[T], <a name="scalation.util.Error" class="extype" href="../util/Error.html">Error</a>, AnyRef, <span name="scala.Any" class="extype">Any</span></div>
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                <ol id="linearization"><li name="scalation.math.MatrixN" class="in"><span>MatrixN</span></li><li name="scalation.math.Matrix" class="in"><span>Matrix</span></li><li name="scalation.util.Error" class="in"><span>Error</span></li><li name="scala.AnyRef" class="in"><span>AnyRef</span></li><li name="scala.Any" class="in"><span>Any</span></li></ol>
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        <div class="members" id="constructors">
              <h3>Instance Constructors</h3>
              <ol><li visbl="pub" name="scalation.math.MatrixN#this" data-isabs="false">
      <a id="this:MatrixN[T]"></a>
      <h4 class="signature">
      <span class="kind">new</span>
      <span class="symbol"> 
        <span class="name">MatrixN</span>
        
        <span class="params">(<span name="u">u: <a name="scalation.math.MatrixN" class="extype" href="">MatrixN</a>[T]</span>)</span><span class="params">(<span class="implicit">implicit </span><span name="arg0">arg0: (T) ⇒ Ordered[T]</span>, <span name="arg1">arg1: ClassManifest[T]</span>, <span name="arg2">arg2: Numeric[T]</span>)</span>
      </span>
      </h4>
      <p class="shortcomment cmt">:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Construct a matrix and assign values from matrix u.</p><div class="fullcomment"><div class="comment cmt"><p>:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Construct a matrix and assign values from matrix u.</p></div><dl class="paramcmts block"><dt class="param">u</dt><dd class="cmt"><p>the matrix of values to assign
</p></dd></dl></div>
    </li><li visbl="pub" name="scalation.math.MatrixN#this" data-isabs="false">
      <a id="this:MatrixN[T]"></a>
      <h4 class="signature">
      <span class="kind">new</span>
      <span class="symbol"> 
        <span class="name">MatrixN</span>
        
        <span class="params">(<span name="u">u: <span name="scala.Array" class="extype">Array</span>[<a name="scalation.math.VectorN" class="extype" href="VectorN.html">VectorN</a>[T]]</span>)</span><span class="params">(<span class="implicit">implicit </span><span name="arg0">arg0: (T) ⇒ Ordered[T]</span>, <span name="arg1">arg1: ClassManifest[T]</span>, <span name="arg2">arg2: Numeric[T]</span>)</span>
      </span>
      </h4>
      <p class="shortcomment cmt">:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Construct a matrix and assign values from array of vectors u.</p><div class="fullcomment"><div class="comment cmt"><p>:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Construct a matrix and assign values from array of vectors u.</p></div><dl class="paramcmts block"><dt class="param">u</dt><dd class="cmt"><p>the 2D array of values to assign
</p></dd></dl></div>
    </li><li visbl="pub" name="scalation.math.MatrixN#this" data-isabs="false">
      <a id="this:MatrixN[T]"></a>
      <h4 class="signature">
      <span class="kind">new</span>
      <span class="symbol"> 
        <span class="name">MatrixN</span>
        
        <span class="params">(<span name="dim">dim: (<span name="scala.Int" class="extype">Int</span>, <span name="scala.Int" class="extype">Int</span>)</span>, <span name="u">u: T*</span>)</span><span class="params">(<span class="implicit">implicit </span><span name="arg0">arg0: (T) ⇒ Ordered[T]</span>, <span name="arg1">arg1: ClassManifest[T]</span>, <span name="arg2">arg2: Numeric[T]</span>)</span>
      </span>
      </h4>
      <p class="shortcomment cmt">:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Construct a matrix from repeated values.</p><div class="fullcomment"><div class="comment cmt"><p>:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Construct a matrix from repeated values.</p></div><dl class="paramcmts block"><dt class="param">dim</dt><dd class="cmt"><p>the (row, column) dimensions</p></dd><dt class="param">u</dt><dd class="cmt"><p>the repeated values
</p></dd></dl></div>
    </li><li visbl="pub" name="scalation.math.MatrixN#this" data-isabs="false">
      <a id="this:MatrixN[T]"></a>
      <h4 class="signature">
      <span class="kind">new</span>
      <span class="symbol"> 
        <span class="name">MatrixN</span>
        
        <span class="params">(<span name="u">u: <span name="scala.Array" class="extype">Array</span>[<span name="scala.Array" class="extype">Array</span>[T]]</span>)</span><span class="params">(<span class="implicit">implicit </span><span name="arg0">arg0: (T) ⇒ Ordered[T]</span>, <span name="arg1">arg1: ClassManifest[T]</span>, <span name="arg2">arg2: Numeric[T]</span>)</span>
      </span>
      </h4>
      <p class="shortcomment cmt">:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Construct a matrix and assign values from array of arrays u.</p><div class="fullcomment"><div class="comment cmt"><p>:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Construct a matrix and assign values from array of arrays u.</p></div><dl class="paramcmts block"><dt class="param">u</dt><dd class="cmt"><p>the 2D array of values to assign
</p></dd></dl></div>
    </li><li visbl="pub" name="scalation.math.MatrixN#this" data-isabs="false">
      <a id="this:MatrixN[T]"></a>
      <h4 class="signature">
      <span class="kind">new</span>
      <span class="symbol"> 
        <span class="name">MatrixN</span>
        
        <span class="params">(<span name="dim1">dim1: <span name="scala.Int" class="extype">Int</span></span>, <span name="x">x: T</span>, <span name="y">y: T</span>)</span><span class="params">(<span class="implicit">implicit </span><span name="arg0">arg0: (T) ⇒ Ordered[T]</span>, <span name="arg1">arg1: ClassManifest[T]</span>, <span name="arg2">arg2: Numeric[T]</span>)</span>
      </span>
      </h4>
      <p class="shortcomment cmt">:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Construct a dim1 by dim1 square matrix with x assigned on the diagonal
and y assigned off the diagonal.</p><div class="fullcomment"><div class="comment cmt"><p>:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Construct a dim1 by dim1 square matrix with x assigned on the diagonal
and y assigned off the diagonal.  To obtain an identity matrix, let x = 1
and y = 0.</p></div><dl class="paramcmts block"><dt class="param">dim1</dt><dd class="cmt"><p>the row and column dimension</p></dd><dt class="param">x</dt><dd class="cmt"><p>the scalar value to assign on the diagonal</p></dd><dt class="param">y</dt><dd class="cmt"><p>the scalar value to assign off the diagonal
</p></dd></dl></div>
    </li><li visbl="pub" name="scalation.math.MatrixN#this" data-isabs="false">
      <a id="this:MatrixN[T]"></a>
      <h4 class="signature">
      <span class="kind">new</span>
      <span class="symbol"> 
        <span class="name">MatrixN</span>
        
        <span class="params">(<span name="dim1">dim1: <span name="scala.Int" class="extype">Int</span></span>, <span name="dim2">dim2: <span name="scala.Int" class="extype">Int</span></span>, <span name="x">x: T</span>)</span><span class="params">(<span class="implicit">implicit </span><span name="arg0">arg0: (T) ⇒ Ordered[T]</span>, <span name="arg1">arg1: ClassManifest[T]</span>, <span name="arg2">arg2: Numeric[T]</span>)</span>
      </span>
      </h4>
      <p class="shortcomment cmt">:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Construct a dim1 by dim2 matrix and assign each element the value x.</p><div class="fullcomment"><div class="comment cmt"><p>:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Construct a dim1 by dim2 matrix and assign each element the value x.</p></div><dl class="paramcmts block"><dt class="param">dim1</dt><dd class="cmt"><p>the row dimension</p></dd><dt class="param">dim2</dt><dd class="cmt"><p>the column dimesion</p></dd><dt class="param">x</dt><dd class="cmt"><p>the scalar value to assign
</p></dd></dl></div>
    </li><li visbl="pub" name="scalation.math.MatrixN#this" data-isabs="false">
      <a id="this:MatrixN[T]"></a>
      <h4 class="signature">
      <span class="kind">new</span>
      <span class="symbol"> 
        <span class="name">MatrixN</span>
        
        <span class="params">(<span name="dim1">dim1: <span name="scala.Int" class="extype">Int</span></span>)</span><span class="params">(<span class="implicit">implicit </span><span name="arg0">arg0: (T) ⇒ Ordered[T]</span>, <span name="arg1">arg1: ClassManifest[T]</span>, <span name="arg2">arg2: Numeric[T]</span>)</span>
      </span>
      </h4>
      <p class="shortcomment cmt">:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Construct a dim1 by dim1 square matrix.</p><div class="fullcomment"><div class="comment cmt"><p>:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Construct a dim1 by dim1 square matrix.</p></div><dl class="paramcmts block"><dt class="param">dim1</dt><dd class="cmt"><p>the row and column dimension
</p></dd></dl></div>
    </li><li visbl="pub" name="scalation.math.MatrixN#this" data-isabs="false">
      <a id="this:MatrixN[T]"></a>
      <h4 class="signature">
      <span class="kind">new</span>
      <span class="symbol"> 
        <span class="name">MatrixN</span>
        
        <span class="params">(<span name="d1">d1: <span name="scala.Int" class="extype">Int</span></span>, <span name="d2">d2: <span name="scala.Int" class="extype">Int</span></span>, <span name="v">v: <span name="scala.Array" class="extype">Array</span>[<span name="scala.Array" class="extype">Array</span>[T]]</span>)</span><span class="params">(<span class="implicit">implicit </span><span name="arg0">arg0: (T) ⇒ Ordered[T]</span>, <span name="arg1">arg1: ClassManifest[T]</span>, <span name="arg2">arg2: Numeric[T]</span>)</span>
      </span>
      </h4>
      <p class="shortcomment cmt"></p><div class="fullcomment"><div class="comment cmt"></div><dl class="paramcmts block"><dt class="param">v</dt><dd class="cmt"><p>the 2D array used to store matrix elements
</p></dd></dl></div>
    </li></ol>
            </div>

        
        
        

        <div class="values members" id="values">
              <h3>Value Members</h3>
              <ol><li visbl="pub" name="scala.AnyRef#!=" data-isabs="false">
      <a id="!=(AnyRef):Boolean"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">!=</span>
        
        <span class="params">(<span name="arg0">arg0: AnyRef</span>)</span><span class="result">: <span name="scala.Boolean" class="extype">Boolean</span></span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Attributes</dt><dd>final </dd><dt>Definition Classes</dt><dd>AnyRef</dd></dl></div>
    </li><li visbl="pub" name="scala.Any#!=" data-isabs="false">
      <a id="!=(Any):Boolean"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">!=</span>
        
        <span class="params">(<span name="arg0">arg0: <span name="scala.Any" class="extype">Any</span></span>)</span><span class="result">: <span name="scala.Boolean" class="extype">Boolean</span></span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Attributes</dt><dd>final </dd><dt>Definition Classes</dt><dd>Any</dd></dl></div>
    </li><li visbl="pub" name="scala.AnyRef###" data-isabs="false">
      <a id="##():Int"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">##</span>
        
        <span class="params">()</span><span class="result">: <span name="scala.Int" class="extype">Int</span></span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Attributes</dt><dd>final </dd><dt>Definition Classes</dt><dd>AnyRef → Any</dd></dl></div>
    </li><li visbl="pub" name="scalation.math.MatrixN#*" data-isabs="false">
      <a id="*(T):MatrixN[T]"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">*</span>
        
        <span class="params">(<span name="s">s: T</span>)</span><span class="result">: <a name="scalation.math.MatrixN" class="extype" href="">MatrixN</a>[T]</span>
      </span>
      </h4>
      <p class="shortcomment cmt">:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Multiply this matrix by scalar s.</p><div class="fullcomment"><div class="comment cmt"><p>:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Multiply this matrix by scalar s.</p></div><dl class="paramcmts block"><dt class="param">s</dt><dd class="cmt"><p>the scalar to multiply by
</p></dd></dl><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="scalation.math.MatrixN" class="extype" href="">MatrixN</a> → <a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a></dd></dl></div>
    </li><li visbl="pub" name="scalation.math.MatrixN#*" data-isabs="false">
      <a id="*(VectorN[T]):VectorN[T]"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">*</span>
        
        <span class="params">(<span name="b">b: <a name="scalation.math.VectorN" class="extype" href="VectorN.html">VectorN</a>[T]</span>)</span><span class="result">: <a name="scalation.math.VectorN" class="extype" href="VectorN.html">VectorN</a>[T]</span>
      </span>
      </h4>
      <p class="shortcomment cmt">:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Multiply this matrix by vector b.</p><div class="fullcomment"><div class="comment cmt"><p>:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Multiply this matrix by vector b.</p></div><dl class="paramcmts block"><dt class="param">b</dt><dd class="cmt"><p>the vector to multiply by
</p></dd></dl><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="scalation.math.MatrixN" class="extype" href="">MatrixN</a> → <a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a></dd></dl></div>
    </li><li visbl="pub" name="scalation.math.MatrixN#*" data-isabs="false">
      <a id="*(Matrix[T]):MatrixN[T]"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">*</span>
        
        <span class="params">(<span name="b">b: <a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a>[T]</span>)</span><span class="result">: <a name="scalation.math.MatrixN" class="extype" href="">MatrixN</a>[T]</span>
      </span>
      </h4>
      <p class="shortcomment cmt">:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Multiply this matrix by matrix b.</p><div class="fullcomment"><div class="comment cmt"><p>:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Multiply this matrix by matrix b.</p></div><dl class="paramcmts block"><dt class="param">b</dt><dd class="cmt"><p>the matrix to multiply by (requires sameCrossDimensions)
</p></dd></dl><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="scalation.math.MatrixN" class="extype" href="">MatrixN</a> → <a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a></dd></dl></div>
    </li><li visbl="pub" name="scalation.math.MatrixN#**" data-isabs="false">
      <a id="**(VectorN[T]):MatrixN[T]"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">**</span>
        
        <span class="params">(<span name="b">b: <a name="scalation.math.VectorN" class="extype" href="VectorN.html">VectorN</a>[T]</span>)</span><span class="result">: <a name="scalation.math.MatrixN" class="extype" href="">MatrixN</a>[T]</span>
      </span>
      </h4>
      <p class="shortcomment cmt">:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Multiply this matrix by vector b to produce another matrix (a_ij * b_j)</p><div class="fullcomment"><div class="comment cmt"><p>:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Multiply this matrix by vector b to produce another matrix (a_ij * b_j)</p></div><dl class="paramcmts block"><dt class="param">b</dt><dd class="cmt"><p>the vector to multiply by
</p></dd></dl><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="scalation.math.MatrixN" class="extype" href="">MatrixN</a> → <a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a></dd></dl></div>
    </li><li visbl="pub" name="scalation.math.MatrixN#**=" data-isabs="false">
      <a id="**=(VectorN[T]):Unit"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">**=</span>
        
        <span class="params">(<span name="b">b: <a name="scalation.math.VectorN" class="extype" href="VectorN.html">VectorN</a>[T]</span>)</span><span class="result">: <span name="scala.Unit" class="extype">Unit</span></span>
      </span>
      </h4>
      <p class="shortcomment cmt">:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Multiply inplace this matrix by vector b to produce another matrix (a_ij * b_j)</p><div class="fullcomment"><div class="comment cmt"><p>:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Multiply inplace this matrix by vector b to produce another matrix (a_ij * b_j)</p></div><dl class="paramcmts block"><dt class="param">b</dt><dd class="cmt"><p>the vector to multiply by
</p></dd></dl><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="scalation.math.MatrixN" class="extype" href="">MatrixN</a> → <a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a></dd></dl></div>
    </li><li visbl="pub" name="scalation.math.MatrixN#*=" data-isabs="false">
      <a id="*=(T):Unit"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">*=</span>
        
        <span class="params">(<span name="s">s: T</span>)</span><span class="result">: <span name="scala.Unit" class="extype">Unit</span></span>
      </span>
      </h4>
      <p class="shortcomment cmt">:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Multiply inplace this matrix by scalar s.</p><div class="fullcomment"><div class="comment cmt"><p>:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Multiply inplace this matrix by scalar s.</p></div><dl class="paramcmts block"><dt class="param">s</dt><dd class="cmt"><p>the scalar to multiply by
</p></dd></dl><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="scalation.math.MatrixN" class="extype" href="">MatrixN</a> → <a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a></dd></dl></div>
    </li><li visbl="pub" name="scalation.math.MatrixN#*=" data-isabs="false">
      <a id="*=(Matrix[T]):Unit"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">*=</span>
        
        <span class="params">(<span name="b">b: <a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a>[T]</span>)</span><span class="result">: <span name="scala.Unit" class="extype">Unit</span></span>
      </span>
      </h4>
      <p class="shortcomment cmt">:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Multiply inplace this matrix by matrix b.</p><div class="fullcomment"><div class="comment cmt"><p>:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Multiply inplace this matrix by matrix b.</p></div><dl class="paramcmts block"><dt class="param">b</dt><dd class="cmt"><p>the matrix to multiply by (requires sameCrossDimensions)
</p></dd></dl><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="scalation.math.MatrixN" class="extype" href="">MatrixN</a> → <a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a></dd></dl></div>
    </li><li visbl="pub" name="scalation.math.MatrixN#+" data-isabs="false">
      <a id="+(T):MatrixN[T]"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">+</span>
        
        <span class="params">(<span name="s">s: T</span>)</span><span class="result">: <a name="scalation.math.MatrixN" class="extype" href="">MatrixN</a>[T]</span>
      </span>
      </h4>
      <p class="shortcomment cmt">:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Add this matrix and scalar s.</p><div class="fullcomment"><div class="comment cmt"><p>:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Add this matrix and scalar s.</p></div><dl class="paramcmts block"><dt class="param">s</dt><dd class="cmt"><p>the scalar to add
</p></dd></dl><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="scalation.math.MatrixN" class="extype" href="">MatrixN</a> → <a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a></dd></dl></div>
    </li><li visbl="pub" name="scalation.math.MatrixN#+" data-isabs="false">
      <a id="+(Matrix[T]):MatrixN[T]"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">+</span>
        
        <span class="params">(<span name="b">b: <a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a>[T]</span>)</span><span class="result">: <a name="scalation.math.MatrixN" class="extype" href="">MatrixN</a>[T]</span>
      </span>
      </h4>
      <p class="shortcomment cmt">:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Add this matrix and matrix b.</p><div class="fullcomment"><div class="comment cmt"><p>:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Add this matrix and matrix b.</p></div><dl class="paramcmts block"><dt class="param">b</dt><dd class="cmt"><p>the matrix to add (requires sameCrossDimensions)
</p></dd></dl><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="scalation.math.MatrixN" class="extype" href="">MatrixN</a> → <a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a></dd></dl></div>
    </li><li visbl="pub" name="scalation.math.MatrixN#++" data-isabs="false">
      <a id="++(VectorN[T]):MatrixN[T]"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">++</span>
        
        <span class="params">(<span name="b">b: <a name="scalation.math.VectorN" class="extype" href="VectorN.html">VectorN</a>[T]</span>)</span><span class="result">: <a name="scalation.math.MatrixN" class="extype" href="">MatrixN</a>[T]</span>
      </span>
      </h4>
      <p class="shortcomment cmt">Concatenate this matrix and vector b.</p><div class="fullcomment"><div class="comment cmt"><p>Concatenate this matrix and vector b.</p></div><dl class="paramcmts block"><dt class="param">b</dt><dd class="cmt"><p>the vector to be concatenated as the new last row in matrix
</p></dd></dl></div>
    </li><li visbl="pub" name="scalation.math.MatrixN#+=" data-isabs="false">
      <a id="+=(T):Unit"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">+=</span>
        
        <span class="params">(<span name="s">s: T</span>)</span><span class="result">: <span name="scala.Unit" class="extype">Unit</span></span>
      </span>
      </h4>
      <p class="shortcomment cmt">:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Add inplace this matrix and scalar s.</p><div class="fullcomment"><div class="comment cmt"><p>:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Add inplace this matrix and scalar s.</p></div><dl class="paramcmts block"><dt class="param">s</dt><dd class="cmt"><p>the scalar to add
</p></dd></dl><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="scalation.math.MatrixN" class="extype" href="">MatrixN</a> → <a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a></dd></dl></div>
    </li><li visbl="pub" name="scalation.math.MatrixN#+=" data-isabs="false">
      <a id="+=(Matrix[T]):Unit"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">+=</span>
        
        <span class="params">(<span name="b">b: <a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a>[T]</span>)</span><span class="result">: <span name="scala.Unit" class="extype">Unit</span></span>
      </span>
      </h4>
      <p class="shortcomment cmt">:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Add inplace this matrix and matrix b.</p><div class="fullcomment"><div class="comment cmt"><p>:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Add inplace this matrix and matrix b.</p></div><dl class="paramcmts block"><dt class="param">b</dt><dd class="cmt"><p>the matrix to add (requires sameCrossDimensions)
</p></dd></dl><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="scalation.math.MatrixN" class="extype" href="">MatrixN</a> → <a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a></dd></dl></div>
    </li><li visbl="pub" name="scalation.math.MatrixN#-" data-isabs="false">
      <a id="-(T):MatrixN[T]"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">-</span>
        
        <span class="params">(<span name="s">s: T</span>)</span><span class="result">: <a name="scalation.math.MatrixN" class="extype" href="">MatrixN</a>[T]</span>
      </span>
      </h4>
      <p class="shortcomment cmt">:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
From this matrix subtract scalar s.</p><div class="fullcomment"><div class="comment cmt"><p>:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
From this matrix subtract scalar s.</p></div><dl class="paramcmts block"><dt class="param">s</dt><dd class="cmt"><p>the scalar to subtract
</p></dd></dl><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="scalation.math.MatrixN" class="extype" href="">MatrixN</a> → <a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a></dd></dl></div>
    </li><li visbl="pub" name="scalation.math.MatrixN#-" data-isabs="false">
      <a id="-(Matrix[T]):MatrixN[T]"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">-</span>
        
        <span class="params">(<span name="b">b: <a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a>[T]</span>)</span><span class="result">: <a name="scalation.math.MatrixN" class="extype" href="">MatrixN</a>[T]</span>
      </span>
      </h4>
      <p class="shortcomment cmt">:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
From this matrix substract matrix b.</p><div class="fullcomment"><div class="comment cmt"><p>:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
From this matrix substract matrix b.</p></div><dl class="paramcmts block"><dt class="param">b</dt><dd class="cmt"><p>the matrix to subtract (requires sameCrossDimensions)
</p></dd></dl><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="scalation.math.MatrixN" class="extype" href="">MatrixN</a> → <a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a></dd></dl></div>
    </li><li visbl="pub" name="scalation.math.MatrixN#-=" data-isabs="false">
      <a id="-=(T):Unit"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">-=</span>
        
        <span class="params">(<span name="s">s: T</span>)</span><span class="result">: <span name="scala.Unit" class="extype">Unit</span></span>
      </span>
      </h4>
      <p class="shortcomment cmt">:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
From this matrix subtract inplace scalar s.</p><div class="fullcomment"><div class="comment cmt"><p>:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
From this matrix subtract inplace scalar s.</p></div><dl class="paramcmts block"><dt class="param">s</dt><dd class="cmt"><p>the scalar to subtract
</p></dd></dl><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="scalation.math.MatrixN" class="extype" href="">MatrixN</a> → <a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a></dd></dl></div>
    </li><li visbl="pub" name="scalation.math.MatrixN#-=" data-isabs="false">
      <a id="-=(Matrix[T]):Unit"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">-=</span>
        
        <span class="params">(<span name="b">b: <a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a>[T]</span>)</span><span class="result">: <span name="scala.Unit" class="extype">Unit</span></span>
      </span>
      </h4>
      <p class="shortcomment cmt">:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
From this matrix substract inplace matrix b.</p><div class="fullcomment"><div class="comment cmt"><p>:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
From this matrix substract inplace matrix b.</p></div><dl class="paramcmts block"><dt class="param">b</dt><dd class="cmt"><p>the matrix to subtract (requires sameCrossDimensions)
</p></dd></dl><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="scalation.math.MatrixN" class="extype" href="">MatrixN</a> → <a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a></dd></dl></div>
    </li><li visbl="pub" name="scalation.math.MatrixN#/" data-isabs="false">
      <a id="/(T)(Fractional[T]):MatrixN[T]"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">/</span>
        
        <span class="params">(<span name="s">s: T</span>)</span><span class="params">(<span class="implicit">implicit </span><span name="fr">fr: Fractional[T]</span>)</span><span class="result">: <a name="scalation.math.MatrixN" class="extype" href="">MatrixN</a>[T]</span>
      </span>
      </h4>
      <p class="shortcomment cmt">:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Divide this matrix by scalar s.</p><div class="fullcomment"><div class="comment cmt"><p>:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Divide this matrix by scalar s.</p></div><dl class="paramcmts block"><dt class="param">s</dt><dd class="cmt"><p>the scalar to divide by
</p></dd></dl></div>
    </li><li visbl="pub" name="scalation.math.MatrixN#/=" data-isabs="false">
      <a id="/=(T)(Fractional[T]):Unit"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">/=</span>
        
        <span class="params">(<span name="s">s: T</span>)</span><span class="params">(<span class="implicit">implicit </span><span name="fr">fr: Fractional[T]</span>)</span><span class="result">: <span name="scala.Unit" class="extype">Unit</span></span>
      </span>
      </h4>
      <p class="shortcomment cmt">:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Divide inplace this matrix by scalar s.</p><div class="fullcomment"><div class="comment cmt"><p>:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Divide inplace this matrix by scalar s.</p></div><dl class="paramcmts block"><dt class="param">s</dt><dd class="cmt"><p>the scalar to divide by
</p></dd></dl></div>
    </li><li visbl="pub" name="scala.AnyRef#==" data-isabs="false">
      <a id="==(AnyRef):Boolean"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">==</span>
        
        <span class="params">(<span name="arg0">arg0: AnyRef</span>)</span><span class="result">: <span name="scala.Boolean" class="extype">Boolean</span></span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Attributes</dt><dd>final </dd><dt>Definition Classes</dt><dd>AnyRef</dd></dl></div>
    </li><li visbl="pub" name="scala.Any#==" data-isabs="false">
      <a id="==(Any):Boolean"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">==</span>
        
        <span class="params">(<span name="arg0">arg0: <span name="scala.Any" class="extype">Any</span></span>)</span><span class="result">: <span name="scala.Boolean" class="extype">Boolean</span></span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Attributes</dt><dd>final </dd><dt>Definition Classes</dt><dd>Any</dd></dl></div>
    </li><li visbl="pub" name="scalation.math.MatrixN#apply" data-isabs="false">
      <a id="apply(Int):VectorN[T]"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">apply</span>
        
        <span class="params">(<span name="i">i: <span name="scala.Int" class="extype">Int</span></span>)</span><span class="result">: <a name="scalation.math.VectorN" class="extype" href="VectorN.html">VectorN</a>[T]</span>
      </span>
      </h4>
      <p class="shortcomment cmt">:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Get this matrix's vector at the i-th index position (i-th row).</p><div class="fullcomment"><div class="comment cmt"><p>:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Get this matrix's vector at the i-th index position (i-th row).</p></div><dl class="paramcmts block"><dt class="param">i</dt><dd class="cmt"><p>the row index
</p></dd></dl><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="scalation.math.MatrixN" class="extype" href="">MatrixN</a> → <a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a></dd></dl></div>
    </li><li visbl="pub" name="scalation.math.MatrixN#apply" data-isabs="false">
      <a id="apply(Int,Int):T"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">apply</span>
        
        <span class="params">(<span name="i">i: <span name="scala.Int" class="extype">Int</span></span>, <span name="j">j: <span name="scala.Int" class="extype">Int</span></span>)</span><span class="result">: T</span>
      </span>
      </h4>
      <p class="shortcomment cmt">:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Get this matrix's element at the i,j-th index position.</p><div class="fullcomment"><div class="comment cmt"><p>:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Get this matrix's element at the i,j-th index position.</p></div><dl class="paramcmts block"><dt class="param">i</dt><dd class="cmt"><p>the row index</p></dd><dt class="param">j</dt><dd class="cmt"><p>the column index
</p></dd></dl><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="scalation.math.MatrixN" class="extype" href="">MatrixN</a> → <a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a></dd></dl></div>
    </li><li visbl="pub" name="scala.Any#asInstanceOf" data-isabs="false">
      <a id="asInstanceOf[T0]:T0"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">asInstanceOf</span>
        <span class="tparams">[<span name="T0">T0</span>]</span>
        <span class="result">: T0</span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Attributes</dt><dd>final </dd><dt>Definition Classes</dt><dd>Any</dd></dl></div>
    </li><li visbl="prt" name="scala.AnyRef#clone" data-isabs="false">
      <a id="clone():AnyRef"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">clone</span>
        
        <span class="params">()</span><span class="result">: AnyRef</span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Attributes</dt><dd>protected[<a name="java.lang" class="extype" href="../../java/lang/package.html">lang</a>] </dd><dt>Definition Classes</dt><dd>AnyRef</dd><dt>Annotations</dt><dd>
                <span class="name">@throws</span><span class="args">()</span>
              
        </dd></dl></div>
    </li><li visbl="pub" name="scalation.math.Matrix#col" data-isabs="false">
      <a id="col(Int,Int):VectorN[T]"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">col</span>
        
        <span class="params">(<span name="_col">_col: <span name="scala.Int" class="extype">Int</span></span>, <span name="from">from: <span name="scala.Int" class="extype">Int</span> = <span class="symbol">0</span></span>)</span><span class="result">: <a name="scalation.math.VectorN" class="extype" href="VectorN.html">VectorN</a>[T]</span>
      </span>
      </h4>
      <p class="shortcomment cmt">Get column '_col' from the matrix, returning it as a vector.</p><div class="fullcomment"><div class="comment cmt"><p>Get column '_col' from the matrix, returning it as a vector.</p></div><dl class="paramcmts block"><dt class="param">_col</dt><dd class="cmt"><p>the column to extract from the matrix</p></dd><dt class="param">from</dt><dd class="cmt"><p>the position to start extracting from
</p></dd></dl><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a></dd></dl></div>
    </li><li visbl="pub" name="scalation.math.MatrixN#det" data-isabs="false">
      <a id="det:T"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">det</span>
        
        <span class="result">: T</span>
      </span>
      </h4>
      <p class="shortcomment cmt">:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Compute the determinant of this matrix.</p><div class="fullcomment"><div class="comment cmt"><p>:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Compute the determinant of this matrix.
</p></div><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="scalation.math.MatrixN" class="extype" href="">MatrixN</a> → <a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a></dd></dl></div>
    </li><li visbl="pub" name="scalation.math.MatrixN#diag" data-isabs="false">
      <a id="diag(Int,Int):MatrixN[T]"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">diag</span>
        
        <span class="params">(<span name="p">p: <span name="scala.Int" class="extype">Int</span></span>, <span name="q">q: <span name="scala.Int" class="extype">Int</span></span>)</span><span class="result">: <a name="scalation.math.MatrixN" class="extype" href="">MatrixN</a>[T]</span>
      </span>
      </h4>
      <p class="shortcomment cmt">:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Form a matrix [Ip, this, Iq] where Ir is a r by r identity matrix, by
positioning the three matrices Ip, this and Iq along the diagonal.</p><div class="fullcomment"><div class="comment cmt"><p>:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Form a matrix [Ip, this, Iq] where Ir is a r by r identity matrix, by
positioning the three matrices Ip, this and Iq along the diagonal.</p></div><dl class="paramcmts block"><dt class="param">p</dt><dd class="cmt"><p>the size of identity matrix Ip</p></dd><dt class="param">q</dt><dd class="cmt"><p>the size of identity matrix Iq
</p></dd></dl><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="scalation.math.MatrixN" class="extype" href="">MatrixN</a> → <a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a></dd></dl></div>
    </li><li visbl="pub" name="scalation.math.MatrixN#diag" data-isabs="false">
      <a id="diag(Matrix[T]):MatrixN[T]"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">diag</span>
        
        <span class="params">(<span name="b">b: <a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a>[T]</span>)</span><span class="result">: <a name="scalation.math.MatrixN" class="extype" href="">MatrixN</a>[T]</span>
      </span>
      </h4>
      <p class="shortcomment cmt">:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Combine this matrix with matrix b, placing them along the diagonal and
filling in the bottom left and top right regions with zeroes; [this, b].</p><div class="fullcomment"><div class="comment cmt"><p>:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Combine this matrix with matrix b, placing them along the diagonal and
filling in the bottom left and top right regions with zeroes; [this, b].</p></div><dl class="paramcmts block"><dt class="param">b</dt><dd class="cmt"><p>the matrix to combine with this matrix
</p></dd></dl><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="scalation.math.MatrixN" class="extype" href="">MatrixN</a> → <a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a></dd></dl></div>
    </li><li visbl="pub" name="scalation.math.Matrix#dim1" data-isabs="false">
      <a id="dim1:Int"></a>
      <h4 class="signature">
      <span class="kind">val</span>
      <span class="symbol"> 
        <span class="name">dim1</span>
        
        <span class="result">: <span name="scala.Int" class="extype">Int</span></span>
      </span>
      </h4>
      <p class="shortcomment cmt">the first/row dimension</p><div class="fullcomment"><div class="comment cmt"><p>the first/row dimension</p></div><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a></dd></dl></div>
    </li><li visbl="pub" name="scalation.math.Matrix#dim2" data-isabs="false">
      <a id="dim2:Int"></a>
      <h4 class="signature">
      <span class="kind">val</span>
      <span class="symbol"> 
        <span class="name">dim2</span>
        
        <span class="result">: <span name="scala.Int" class="extype">Int</span></span>
      </span>
      </h4>
      <p class="shortcomment cmt">the second/column dimension</p><div class="fullcomment"><div class="comment cmt"><p>the second/column dimension</p></div><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a></dd></dl></div>
    </li><li visbl="pub" name="scala.AnyRef#eq" data-isabs="false">
      <a id="eq(AnyRef):Boolean"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">eq</span>
        
        <span class="params">(<span name="arg0">arg0: AnyRef</span>)</span><span class="result">: <span name="scala.Boolean" class="extype">Boolean</span></span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Attributes</dt><dd>final </dd><dt>Definition Classes</dt><dd>AnyRef</dd></dl></div>
    </li><li visbl="pub" name="scala.AnyRef#equals" data-isabs="false">
      <a id="equals(Any):Boolean"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">equals</span>
        
        <span class="params">(<span name="arg0">arg0: <span name="scala.Any" class="extype">Any</span></span>)</span><span class="result">: <span name="scala.Boolean" class="extype">Boolean</span></span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Definition Classes</dt><dd>AnyRef → Any</dd></dl></div>
    </li><li visbl="prt" name="scala.AnyRef#finalize" data-isabs="false">
      <a id="finalize():Unit"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">finalize</span>
        
        <span class="params">()</span><span class="result">: <span name="scala.Unit" class="extype">Unit</span></span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Attributes</dt><dd>protected[<a name="java.lang" class="extype" href="../../java/lang/package.html">lang</a>] </dd><dt>Definition Classes</dt><dd>AnyRef</dd><dt>Annotations</dt><dd>
                <span class="name">@throws</span><span class="args">()</span>
              
        </dd></dl></div>
    </li><li visbl="pub" name="scalation.util.Error#flaw" data-isabs="false">
      <a id="flaw(String,String):Unit"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">flaw</span>
        
        <span class="params">(<span name="method">method: String</span>, <span name="message">message: String</span>)</span><span class="result">: <span name="scala.Unit" class="extype">Unit</span></span>
      </span>
      </h4>
      <p class="shortcomment cmt">:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Show the flaw by printing the error message.</p><div class="fullcomment"><div class="comment cmt"><p>:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Show the flaw by printing the error message.</p></div><dl class="paramcmts block"><dt class="param">method</dt><dd class="cmt"><p>the method where the error occured</p></dd><dt class="param">message</dt><dd class="cmt"><p>the error message
</p></dd></dl><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="scalation.util.Error" class="extype" href="../util/Error.html">Error</a></dd></dl></div>
    </li><li visbl="pub" name="scalation.math.Matrix#foreach" data-isabs="false">
      <a id="foreach[U]((Array[T]) ⇒ U):Unit"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">foreach</span>
        <span class="tparams">[<span name="U">U</span>]</span>
        <span class="params">(<span name="f">f: (<span name="scala.Array" class="extype">Array</span>[T]) ⇒ U</span>)</span><span class="result">: <span name="scala.Unit" class="extype">Unit</span></span>
      </span>
      </h4>
      <p class="shortcomment cmt">Iterate over the matrix row by row.</p><div class="fullcomment"><div class="comment cmt"><p>Iterate over the matrix row by row.</p></div><dl class="paramcmts block"><dt class="param">f</dt><dd class="cmt"><p>the function to apply
</p></dd></dl><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a></dd></dl></div>
    </li><li visbl="pub" name="scala.AnyRef#getClass" data-isabs="false">
      <a id="getClass():java.lang.Class[_]"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">getClass</span>
        
        <span class="params">()</span><span class="result">: java.lang.Class[_]</span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Attributes</dt><dd>final </dd><dt>Definition Classes</dt><dd>AnyRef</dd></dl></div>
    </li><li visbl="pub" name="scala.AnyRef#hashCode" data-isabs="false">
      <a id="hashCode():Int"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">hashCode</span>
        
        <span class="params">()</span><span class="result">: <span name="scala.Int" class="extype">Int</span></span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Definition Classes</dt><dd>AnyRef → Any</dd></dl></div>
    </li><li visbl="pub" name="scalation.math.MatrixN#inverse" data-isabs="false">
      <a id="inverse(Fractional[T]):MatrixN[T]"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">inverse</span>
        
        <span class="params">(<span class="implicit">implicit </span><span name="fr">fr: Fractional[T]</span>)</span><span class="result">: <a name="scalation.math.MatrixN" class="extype" href="">MatrixN</a>[T]</span>
      </span>
      </h4>
      <p class="shortcomment cmt">:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Invert this matrix (requires a squareMatrix) and use partial pivoting.</p><div class="fullcomment"><div class="comment cmt"><p>:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Invert this matrix (requires a squareMatrix) and use partial pivoting.
</p></div><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="scalation.math.MatrixN" class="extype" href="">MatrixN</a> → <a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a></dd></dl></div>
    </li><li visbl="pub" name="scalation.math.MatrixN#inverse_ip" data-isabs="false">
      <a id="inverse_ip(Fractional[T]):MatrixN[T]"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">inverse_ip</span>
        
        <span class="params">(<span class="implicit">implicit </span><span name="fr">fr: Fractional[T]</span>)</span><span class="result">: <a name="scalation.math.MatrixN" class="extype" href="">MatrixN</a>[T]</span>
      </span>
      </h4>
      <p class="shortcomment cmt">:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Invert inplace this matrix (requires a squareMatrix) and uses partial pivoting.</p><div class="fullcomment"><div class="comment cmt"><p>:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Invert inplace this matrix (requires a squareMatrix) and uses partial pivoting.
</p></div><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="scalation.math.MatrixN" class="extype" href="">MatrixN</a> → <a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a></dd></dl></div>
    </li><li visbl="pub" name="scalation.math.MatrixN#inverse_npp" data-isabs="false">
      <a id="inverse_npp(Fractional[T]):MatrixN[T]"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">inverse_npp</span>
        
        <span class="params">(<span class="implicit">implicit </span><span name="fr">fr: Fractional[T]</span>)</span><span class="result">: <a name="scalation.math.MatrixN" class="extype" href="">MatrixN</a>[T]</span>
      </span>
      </h4>
      <p class="shortcomment cmt">:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Invert this matrix (requires a squareMatrix) and does not use partial pivoting.</p><div class="fullcomment"><div class="comment cmt"><p>:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Invert this matrix (requires a squareMatrix) and does not use partial pivoting.
</p></div><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="scalation.math.MatrixN" class="extype" href="">MatrixN</a> → <a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a></dd></dl></div>
    </li><li visbl="pub" name="scala.Any#isInstanceOf" data-isabs="false">
      <a id="isInstanceOf[T0]:Boolean"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">isInstanceOf</span>
        <span class="tparams">[<span name="T0">T0</span>]</span>
        <span class="result">: <span name="scala.Boolean" class="extype">Boolean</span></span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Attributes</dt><dd>final </dd><dt>Definition Classes</dt><dd>Any</dd></dl></div>
    </li><li visbl="pub" name="scalation.math.Matrix#isNonnegative" data-isabs="false">
      <a id="isNonnegative:Boolean"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">isNonnegative</span>
        
        <span class="result">: <span name="scala.Boolean" class="extype">Boolean</span></span>
      </span>
      </h4>
      <p class="shortcomment cmt">Check whether this matrix is nonnegative (has no negative elements).</p><div class="fullcomment"><div class="comment cmt"><p>Check whether this matrix is nonnegative (has no negative elements).
</p></div><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a></dd></dl></div>
    </li><li visbl="pub" name="scalation.math.MatrixN#isRectangular" data-isabs="false">
      <a id="isRectangular:Boolean"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">isRectangular</span>
        
        <span class="result">: <span name="scala.Boolean" class="extype">Boolean</span></span>
      </span>
      </h4>
      <p class="shortcomment cmt">:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Check whether this matrix is rectangular (all rows have the same number
of columns).</p><div class="fullcomment"><div class="comment cmt"><p>:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Check whether this matrix is rectangular (all rows have the same number
of columns).
</p></div><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="scalation.math.MatrixN" class="extype" href="">MatrixN</a> → <a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a></dd></dl></div>
    </li><li visbl="pub" name="scalation.math.Matrix#isSquare" data-isabs="false">
      <a id="isSquare:Boolean"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">isSquare</span>
        
        <span class="result">: <span name="scala.Boolean" class="extype">Boolean</span></span>
      </span>
      </h4>
      <p class="shortcomment cmt">Check whether this matrix is square (same row and column dimensions).</p><div class="fullcomment"><div class="comment cmt"><p>Check whether this matrix is square (same row and column dimensions).
</p></div><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a></dd></dl></div>
    </li><li visbl="pub" name="scalation.math.Matrix#isSymmetric" data-isabs="false">
      <a id="isSymmetric:Boolean"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">isSymmetric</span>
        
        <span class="result">: <span name="scala.Boolean" class="extype">Boolean</span></span>
      </span>
      </h4>
      <p class="shortcomment cmt">Check whether this matrix is symmetric.</p><div class="fullcomment"><div class="comment cmt"><p>Check whether this matrix is symmetric.
</p></div><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a></dd></dl></div>
    </li><li visbl="pub" name="scalation.math.MatrixN#lud" data-isabs="false">
      <a id="lud(Fractional[T]):(MatrixN[T], MatrixN[T])"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">lud</span>
        
        <span class="params">(<span class="implicit">implicit </span><span name="fr">fr: Fractional[T]</span>)</span><span class="result">: (<a name="scalation.math.MatrixN" class="extype" href="">MatrixN</a>[T], <a name="scalation.math.MatrixN" class="extype" href="">MatrixN</a>[T])</span>
      </span>
      </h4>
      <p class="shortcomment cmt">:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Decompose this matrix into the product of lower and upper triangular
matrices (l, u) using the LU Decomposition algorithm.</p><div class="fullcomment"><div class="comment cmt"><p>:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Decompose this matrix into the product of lower and upper triangular
matrices (l, u) using the LU Decomposition algorithm.  This version uses
partial pivoting.
</p></div><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="scalation.math.MatrixN" class="extype" href="">MatrixN</a> → <a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a></dd></dl></div>
    </li><li visbl="pub" name="scalation.math.MatrixN#lud_ip" data-isabs="false">
      <a id="lud_ip(Fractional[T]):(MatrixN[T], MatrixN[T])"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">lud_ip</span>
        
        <span class="params">(<span class="implicit">implicit </span><span name="fr">fr: Fractional[T]</span>)</span><span class="result">: (<a name="scalation.math.MatrixN" class="extype" href="">MatrixN</a>[T], <a name="scalation.math.MatrixN" class="extype" href="">MatrixN</a>[T])</span>
      </span>
      </h4>
      <p class="shortcomment cmt">:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Decompose inplace this matrix into the product of lower and upper triangular
matrices (l, u) using the LU Decomposition algorithm.</p><div class="fullcomment"><div class="comment cmt"><p>:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Decompose inplace this matrix into the product of lower and upper triangular
matrices (l, u) using the LU Decomposition algorithm.  This version uses
partial pivoting.
</p></div><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="scalation.math.MatrixN" class="extype" href="">MatrixN</a> → <a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a></dd></dl></div>
    </li><li visbl="pub" name="scalation.math.MatrixN#lud_npp" data-isabs="false">
      <a id="lud_npp(Fractional[T]):(MatrixN[T], MatrixN[T])"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">lud_npp</span>
        
        <span class="params">(<span class="implicit">implicit </span><span name="fr">fr: Fractional[T]</span>)</span><span class="result">: (<a name="scalation.math.MatrixN" class="extype" href="">MatrixN</a>[T], <a name="scalation.math.MatrixN" class="extype" href="">MatrixN</a>[T])</span>
      </span>
      </h4>
      <p class="shortcomment cmt">:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Decompose this matrix into the product of upper and lower triangular
matrices (l, u) using the LU Decomposition algorithm.</p><div class="fullcomment"><div class="comment cmt"><p>:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Decompose this matrix into the product of upper and lower triangular
matrices (l, u) using the LU Decomposition algorithm.  This version uses
no partial pivoting.
</p></div></div>
    </li><li visbl="pub" name="scalation.math.MatrixN#max" data-isabs="false">
      <a id="max(Int):T"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">max</span>
        
        <span class="params">(<span name="e">e: <span name="scala.Int" class="extype">Int</span> = <span class="symbol"><span class="name"><a href="Matrix.html#dim1:Int">dim1</a></span></span></span>)</span><span class="result">: T</span>
      </span>
      </h4>
      <p class="shortcomment cmt">Find the maximum element in this matrix.</p><div class="fullcomment"><div class="comment cmt"><p>Find the maximum element in this matrix.</p></div><dl class="paramcmts block"><dt class="param">e</dt><dd class="cmt"><p>the ending row index (exclusive) for the search
</p></dd></dl></div>
    </li><li visbl="pub" name="scalation.math.MatrixN#min" data-isabs="false">
      <a id="min(Int):T"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">min</span>
        
        <span class="params">(<span name="e">e: <span name="scala.Int" class="extype">Int</span> = <span class="symbol"><span class="name"><a href="Matrix.html#dim1:Int">dim1</a></span></span></span>)</span><span class="result">: T</span>
      </span>
      </h4>
      <p class="shortcomment cmt">Find the minimum element in this matrix.</p><div class="fullcomment"><div class="comment cmt"><p>Find the minimum element in this matrix.</p></div><dl class="paramcmts block"><dt class="param">e</dt><dd class="cmt"><p>the ending row index (exclusive) for the search
</p></dd></dl></div>
    </li><li visbl="pub" name="scala.AnyRef#ne" data-isabs="false">
      <a id="ne(AnyRef):Boolean"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">ne</span>
        
        <span class="params">(<span name="arg0">arg0: AnyRef</span>)</span><span class="result">: <span name="scala.Boolean" class="extype">Boolean</span></span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Attributes</dt><dd>final </dd><dt>Definition Classes</dt><dd>AnyRef</dd></dl></div>
    </li><li visbl="pub" name="scala.AnyRef#notify" data-isabs="false">
      <a id="notify():Unit"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">notify</span>
        
        <span class="params">()</span><span class="result">: <span name="scala.Unit" class="extype">Unit</span></span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Attributes</dt><dd>final </dd><dt>Definition Classes</dt><dd>AnyRef</dd></dl></div>
    </li><li visbl="pub" name="scala.AnyRef#notifyAll" data-isabs="false">
      <a id="notifyAll():Unit"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">notifyAll</span>
        
        <span class="params">()</span><span class="result">: <span name="scala.Unit" class="extype">Unit</span></span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Attributes</dt><dd>final </dd><dt>Definition Classes</dt><dd>AnyRef</dd></dl></div>
    </li><li visbl="prt" name="scalation.math.Matrix#nu" data-isabs="false">
      <a id="nu:Numeric[T]"></a>
      <h4 class="signature">
      <span class="kind">val</span>
      <span class="symbol"> 
        <span class="name">nu</span>
        
        <span class="result">: Numeric[T]</span>
      </span>
      </h4>
      <p class="shortcomment cmt">Create and import Numeric evidence
</p><div class="fullcomment"><div class="comment cmt"><p>Create and import Numeric evidence
</p></div><dl class="attributes block"> <dt>Attributes</dt><dd>protected </dd><dt>Definition Classes</dt><dd><a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a></dd></dl></div>
    </li><li visbl="pub" name="scalation.math.Matrix#nullspace" data-isabs="false">
      <a id="nullspace(Fractional[T]):VectorN[T]"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">nullspace</span>
        
        <span class="params">(<span class="implicit">implicit </span><span name="fr">fr: Fractional[T]</span>)</span><span class="result">: <a name="scalation.math.VectorN" class="extype" href="VectorN.html">VectorN</a>[T]</span>
      </span>
      </h4>
      <p class="shortcomment cmt">Compute the (right) nullspace of this m by n matrix (requires n = m + 1)
 by performing Guass-Jordan reduction and extracting the negation of the
 last column augmented by 1.</p><div class="fullcomment"><div class="comment cmt"><p>Compute the (right) nullspace of this m by n matrix (requires n = m + 1)
 by performing Guass-Jordan reduction and extracting the negation of the
 last column augmented by 1.  The nullspace of matrix a is &quot;this vector v
 times any scalar s&quot;, i.e., s*v*a = 0.  The left nullspace of matrix a is
 the same as the right nullspace of a.t (a transpose).
</p></div><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a></dd></dl></div>
    </li><li visbl="pub" name="scalation.math.Matrix#nullspace_ip" data-isabs="false">
      <a id="nullspace_ip(Fractional[T]):VectorN[T]"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">nullspace_ip</span>
        
        <span class="params">(<span class="implicit">implicit </span><span name="fr">fr: Fractional[T]</span>)</span><span class="result">: <a name="scalation.math.VectorN" class="extype" href="VectorN.html">VectorN</a>[T]</span>
      </span>
      </h4>
      <p class="shortcomment cmt">Compute the (right) nullspace inplace of this m by n matrix (requires n = m + 1)
 by performing Guass-Jordan reduction and extracting the negation of the
 last column augmented by 1.</p><div class="fullcomment"><div class="comment cmt"><p>Compute the (right) nullspace inplace of this m by n matrix (requires n = m + 1)
 by performing Guass-Jordan reduction and extracting the negation of the
 last column augmented by 1.  The nullspace of matrix a is &quot;this vector v
 times any scalar s&quot;, i.e., s*v*a = 0.  The left nullspace of matrix a is
 the same as the right nullspace of a.t (a transpose).
</p></div><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a></dd></dl></div>
    </li><li visbl="pub" name="scalation.math.Matrix#oneIf" data-isabs="false">
      <a id="oneIf(Boolean):Int"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">oneIf</span>
        
        <span class="params">(<span name="cond">cond: <span name="scala.Boolean" class="extype">Boolean</span></span>)</span><span class="result">: <span name="scala.Int" class="extype">Int</span></span>
      </span>
      </h4>
      <p class="shortcomment cmt">Return 1 if the condition is true else 0</p><div class="fullcomment"><div class="comment cmt"><p>Return 1 if the condition is true else 0</p></div><dl class="paramcmts block"><dt class="param">cond</dt><dd class="cmt"><p>the condition to evaluate
</p></dd></dl><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a></dd></dl></div>
    </li><li visbl="prt" name="scalation.math.Matrix#range1" data-isabs="false">
      <a id="range1:Range"></a>
      <h4 class="signature">
      <span class="kind">val</span>
      <span class="symbol"> 
        <span class="name">range1</span>
        
        <span class="result">: <span name="scala.collection.immutable.Range" class="extype">Range</span></span>
      </span>
      </h4>
      <p class="shortcomment cmt">Range for the storage array on dimension 1 (rows)
</p><div class="fullcomment"><div class="comment cmt"><p>Range for the storage array on dimension 1 (rows)
</p></div><dl class="attributes block"> <dt>Attributes</dt><dd>protected </dd><dt>Definition Classes</dt><dd><a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a></dd></dl></div>
    </li><li visbl="prt" name="scalation.math.Matrix#range2" data-isabs="false">
      <a id="range2:Range"></a>
      <h4 class="signature">
      <span class="kind">val</span>
      <span class="symbol"> 
        <span class="name">range2</span>
        
        <span class="result">: <span name="scala.collection.immutable.Range" class="extype">Range</span></span>
      </span>
      </h4>
      <p class="shortcomment cmt">Range for the storage array on dimension 2 (columns)
</p><div class="fullcomment"><div class="comment cmt"><p>Range for the storage array on dimension 2 (columns)
</p></div><dl class="attributes block"> <dt>Attributes</dt><dd>protected </dd><dt>Definition Classes</dt><dd><a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a></dd></dl></div>
    </li><li visbl="pub" name="scalation.math.Matrix#rank" data-isabs="false">
      <a id="rank(Fractional[T]):Double"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">rank</span>
        
        <span class="params">(<span class="implicit">implicit </span><span name="fr">fr: Fractional[T]</span>)</span><span class="result">: <span name="scala.Double" class="extype">Double</span></span>
      </span>
      </h4>
      <p class="shortcomment cmt">Determine the rank of this m by n matrix by taking the upper triangular
 matrix from the LU Decomposition and counting the number of non-zero
 diagonal elements.</p><div class="fullcomment"><div class="comment cmt"><p>Determine the rank of this m by n matrix by taking the upper triangular
 matrix from the LU Decomposition and counting the number of non-zero
 diagonal elements.
</p></div><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a></dd></dl></div>
    </li><li visbl="pub" name="scalation.math.MatrixN#reduce" data-isabs="false">
      <a id="reduce(Fractional[T]):MatrixN[T]"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">reduce</span>
        
        <span class="params">(<span class="implicit">implicit </span><span name="fr">fr: Fractional[T]</span>)</span><span class="result">: <a name="scalation.math.MatrixN" class="extype" href="">MatrixN</a>[T]</span>
      </span>
      </h4>
      <p class="shortcomment cmt">:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Use Guass-Jordan reduction on this matrix to make the left part embed an
identity matrix.</p><div class="fullcomment"><div class="comment cmt"><p>:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Use Guass-Jordan reduction on this matrix to make the left part embed an
identity matrix.  A constraint on this m by n matrix is that n &gt;= m.
</p></div><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="scalation.math.MatrixN" class="extype" href="">MatrixN</a> → <a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a></dd></dl></div>
    </li><li visbl="pub" name="scalation.math.MatrixN#reduce_ip" data-isabs="false">
      <a id="reduce_ip(Fractional[T]):Unit"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">reduce_ip</span>
        
        <span class="params">(<span class="implicit">implicit </span><span name="fr">fr: Fractional[T]</span>)</span><span class="result">: <span name="scala.Unit" class="extype">Unit</span></span>
      </span>
      </h4>
      <p class="shortcomment cmt">:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Use Guass-Jordan reduction inplace on this matrix to make the left part
embed an identity matrix.</p><div class="fullcomment"><div class="comment cmt"><p>:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Use Guass-Jordan reduction inplace on this matrix to make the left part
embed an identity matrix.  A constraint on this m by n matrix is that n &gt;= m.
</p></div><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="scalation.math.MatrixN" class="extype" href="">MatrixN</a> → <a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a></dd></dl></div>
    </li><li visbl="pub" name="scalation.math.Matrix#row" data-isabs="false">
      <a id="row(Int,Int):VectorN[T]"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">row</span>
        
        <span class="params">(<span name="_row">_row: <span name="scala.Int" class="extype">Int</span></span>, <span name="from">from: <span name="scala.Int" class="extype">Int</span> = <span class="symbol">0</span></span>)</span><span class="result">: <a name="scalation.math.VectorN" class="extype" href="VectorN.html">VectorN</a>[T]</span>
      </span>
      </h4>
      <p class="shortcomment cmt">Get row '_row' from the matrix, returning it as a vector.</p><div class="fullcomment"><div class="comment cmt"><p>Get row '_row' from the matrix, returning it as a vector.</p></div><dl class="paramcmts block"><dt class="param">_row</dt><dd class="cmt"><p>the row to extract from the matrix</p></dd><dt class="param">from</dt><dd class="cmt"><p>the position to start extracting from
</p></dd></dl><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a></dd></dl></div>
    </li><li visbl="pub" name="scalation.math.Matrix#sameCrossDimensions" data-isabs="false">
      <a id="sameCrossDimensions(Matrix[T]):Boolean"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">sameCrossDimensions</span>
        
        <span class="params">(<span name="b">b: <a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a>[T]</span>)</span><span class="result">: <span name="scala.Boolean" class="extype">Boolean</span></span>
      </span>
      </h4>
      <p class="shortcomment cmt">Check whether this matrix and the other matrix have the same cross dimensions.</p><div class="fullcomment"><div class="comment cmt"><p>Check whether this matrix and the other matrix have the same cross dimensions.</p></div><dl class="paramcmts block"><dt class="param">b</dt><dd class="cmt"><p>the other matrix
</p></dd></dl><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a></dd></dl></div>
    </li><li visbl="pub" name="scalation.math.Matrix#sameDimensions" data-isabs="false">
      <a id="sameDimensions(Matrix[T]):Boolean"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">sameDimensions</span>
        
        <span class="params">(<span name="b">b: <a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a>[T]</span>)</span><span class="result">: <span name="scala.Boolean" class="extype">Boolean</span></span>
      </span>
      </h4>
      <p class="shortcomment cmt">Check whether this matrix and the other Matrix have the same dimensions.</p><div class="fullcomment"><div class="comment cmt"><p>Check whether this matrix and the other Matrix have the same dimensions.</p></div><dl class="paramcmts block"><dt class="param">b</dt><dd class="cmt"><p>the other matrix
</p></dd></dl><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a></dd></dl></div>
    </li><li visbl="pub" name="scalation.math.MatrixN#selectCols" data-isabs="false">
      <a id="selectCols(VectorI):MatrixN[T]"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">selectCols</span>
        
        <span class="params">(<span name="basis">basis: VectorI</span>)</span><span class="result">: <a name="scalation.math.MatrixN" class="extype" href="">MatrixN</a>[T]</span>
      </span>
      </h4>
      <p class="shortcomment cmt">:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Select columns from this matrix according a basis.</p><div class="fullcomment"><div class="comment cmt"><p>:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Select columns from this matrix according a basis.</p></div><dl class="paramcmts block"><dt class="param">basis</dt><dd class="cmt"><p>the column index positions (e.g., (0, 2, 5))
</p></dd></dl></div>
    </li><li visbl="pub" name="scalation.math.MatrixN#selectRows" data-isabs="false">
      <a id="selectRows(VectorI):MatrixN[T]"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">selectRows</span>
        
        <span class="params">(<span name="basis">basis: VectorI</span>)</span><span class="result">: <a name="scalation.math.MatrixN" class="extype" href="">MatrixN</a>[T]</span>
      </span>
      </h4>
      <p class="shortcomment cmt">:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Select rows from this matrix according a basis.</p><div class="fullcomment"><div class="comment cmt"><p>:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Select rows from this matrix according a basis.</p></div><dl class="paramcmts block"><dt class="param">basis</dt><dd class="cmt"><p>the row index positions (e.g., (0, 2, 5))
</p></dd></dl></div>
    </li><li visbl="pub" name="scalation.math.MatrixN#set" data-isabs="false">
      <a id="set(Int,Int,VectorN[T]):Unit"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">set</span>
        
        <span class="params">(<span name="i">i: <span name="scala.Int" class="extype">Int</span></span>, <span name="j">j: <span name="scala.Int" class="extype">Int</span></span>, <span name="u">u: <a name="scalation.math.VectorN" class="extype" href="VectorN.html">VectorN</a>[T]</span>)</span><span class="result">: <span name="scala.Unit" class="extype">Unit</span></span>
      </span>
      </h4>
      <p class="shortcomment cmt">:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Set this matrix's row at the i-th index position to the vector u.</p><div class="fullcomment"><div class="comment cmt"><p>:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Set this matrix's row at the i-th index position to the vector u.</p></div><dl class="paramcmts block"><dt class="param">i</dt><dd class="cmt"><p>the row index</p></dd><dt class="param">j</dt><dd class="cmt"><p>the starting column index</p></dd><dt class="param">u</dt><dd class="cmt"><p>the vector value to assign
</p></dd></dl></div>
    </li><li visbl="pub" name="scalation.math.Matrix#set" data-isabs="false">
      <a id="set(Array[Array[T]]):Unit"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">set</span>
        
        <span class="params">(<span name="u">u: <span name="scala.Array" class="extype">Array</span>[<span name="scala.Array" class="extype">Array</span>[T]]</span>)</span><span class="result">: <span name="scala.Unit" class="extype">Unit</span></span>
      </span>
      </h4>
      <p class="shortcomment cmt">Set the values in this matrix as copies of the values in 2D array u.</p><div class="fullcomment"><div class="comment cmt"><p>Set the values in this matrix as copies of the values in 2D array u.</p></div><dl class="paramcmts block"><dt class="param">u</dt><dd class="cmt"><p>the 2D array of values to assign
</p></dd></dl><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a></dd></dl></div>
    </li><li visbl="pub" name="scalation.math.Matrix#set" data-isabs="false">
      <a id="set(T):Unit"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">set</span>
        
        <span class="params">(<span name="x">x: T</span>)</span><span class="result">: <span name="scala.Unit" class="extype">Unit</span></span>
      </span>
      </h4>
      <p class="shortcomment cmt">Set all the elements in this matrix to the scalar x.</p><div class="fullcomment"><div class="comment cmt"><p>Set all the elements in this matrix to the scalar x.</p></div><dl class="paramcmts block"><dt class="param">x</dt><dd class="cmt"><p>the scalar value to assign
</p></dd></dl><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a></dd></dl></div>
    </li><li visbl="pub" name="scalation.math.Matrix#setCol" data-isabs="false">
      <a id="setCol(Int,VectorN[T]):Unit"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">setCol</span>
        
        <span class="params">(<span name="col">col: <span name="scala.Int" class="extype">Int</span></span>, <span name="u">u: <a name="scalation.math.VectorN" class="extype" href="VectorN.html">VectorN</a>[T]</span>)</span><span class="result">: <span name="scala.Unit" class="extype">Unit</span></span>
      </span>
      </h4>
      <p class="shortcomment cmt">Set column 'col' of the matrix to a vector.</p><div class="fullcomment"><div class="comment cmt"><p>Set column 'col' of the matrix to a vector.</p></div><dl class="paramcmts block"><dt class="param">col</dt><dd class="cmt"><p>the column to set</p></dd><dt class="param">u</dt><dd class="cmt"><p>the vector to assign to the column
</p></dd></dl><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a></dd></dl></div>
    </li><li visbl="pub" name="scalation.math.Matrix#setLower" data-isabs="false">
      <a id="setLower(T):Unit"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">setLower</span>
        
        <span class="params">(<span name="x">x: T</span>)</span><span class="result">: <span name="scala.Unit" class="extype">Unit</span></span>
      </span>
      </h4>
      <p class="shortcomment cmt">Set all the lower triangular elements in this matrix to the scalar x.</p><div class="fullcomment"><div class="comment cmt"><p>Set all the lower triangular elements in this matrix to the scalar x.</p></div><dl class="paramcmts block"><dt class="param">x</dt><dd class="cmt"><p>the scalar value to assign
</p></dd></dl><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a></dd></dl></div>
    </li><li visbl="pub" name="scalation.math.Matrix#setRow" data-isabs="false">
      <a id="setRow(Int,VectorN[T]):Unit"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">setRow</span>
        
        <span class="params">(<span name="row">row: <span name="scala.Int" class="extype">Int</span></span>, <span name="u">u: <a name="scalation.math.VectorN" class="extype" href="VectorN.html">VectorN</a>[T]</span>)</span><span class="result">: <span name="scala.Unit" class="extype">Unit</span></span>
      </span>
      </h4>
      <p class="shortcomment cmt">Set row 'row' of the matrix to a vector.</p><div class="fullcomment"><div class="comment cmt"><p>Set row 'row' of the matrix to a vector.</p></div><dl class="paramcmts block"><dt class="param">row</dt><dd class="cmt"><p>the column to set</p></dd><dt class="param">u</dt><dd class="cmt"><p>the vector to assign to the column
</p></dd></dl><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a></dd></dl></div>
    </li><li visbl="pub" name="scalation.math.MatrixN#slice" data-isabs="false">
      <a id="slice(Int,Int,Int,Int):MatrixN[T]"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">slice</span>
        
        <span class="params">(<span name="r_from">r_from: <span name="scala.Int" class="extype">Int</span></span>, <span name="r_end">r_end: <span name="scala.Int" class="extype">Int</span></span>, <span name="c_from">c_from: <span name="scala.Int" class="extype">Int</span></span>, <span name="c_end">c_end: <span name="scala.Int" class="extype">Int</span></span>)</span><span class="result">: <a name="scalation.math.MatrixN" class="extype" href="">MatrixN</a>[T]</span>
      </span>
      </h4>
      <p class="shortcomment cmt">:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Slice this matrix row-wise r_from to r_end and column-wise c_from to c_end.</p><div class="fullcomment"><div class="comment cmt"><p>:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Slice this matrix row-wise r_from to r_end and column-wise c_from to c_end.</p></div><dl class="paramcmts block"><dt class="param">r_from</dt><dd class="cmt"><p>the start of the row slice</p></dd><dt class="param">r_end</dt><dd class="cmt"><p>the end of the row slice</p></dd><dt class="param">c_from</dt><dd class="cmt"><p>the start of the column slice</p></dd><dt class="param">c_end</dt><dd class="cmt"><p>the end of the column slice
</p></dd></dl><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="scalation.math.MatrixN" class="extype" href="">MatrixN</a> → <a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a></dd></dl></div>
    </li><li visbl="pub" name="scalation.math.MatrixN#slice" data-isabs="false">
      <a id="slice(Int,Int):MatrixN[T]"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">slice</span>
        
        <span class="params">(<span name="from">from: <span name="scala.Int" class="extype">Int</span></span>, <span name="end">end: <span name="scala.Int" class="extype">Int</span></span>)</span><span class="result">: <a name="scalation.math.MatrixN" class="extype" href="">MatrixN</a>[T]</span>
      </span>
      </h4>
      <p class="shortcomment cmt">:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Slice this matrix row-wise from to end.</p><div class="fullcomment"><div class="comment cmt"><p>:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Slice this matrix row-wise from to end.</p></div><dl class="paramcmts block"><dt class="param">from</dt><dd class="cmt"><p>the start row of the slice (inclusive)</p></dd><dt class="param">end</dt><dd class="cmt"><p>the end row of the slice (exclusive)
</p></dd></dl><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="scalation.math.MatrixN" class="extype" href="">MatrixN</a> → <a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a></dd></dl></div>
    </li><li visbl="pub" name="scalation.math.MatrixN#sliceExclude" data-isabs="false">
      <a id="sliceExclude(Int,Int):MatrixN[T]"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">sliceExclude</span>
        
        <span class="params">(<span name="row">row: <span name="scala.Int" class="extype">Int</span></span>, <span name="col">col: <span name="scala.Int" class="extype">Int</span></span>)</span><span class="result">: <a name="scalation.math.MatrixN" class="extype" href="">MatrixN</a>[T]</span>
      </span>
      </h4>
      <p class="shortcomment cmt">:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Slice this matrix excluding the given row and column.</p><div class="fullcomment"><div class="comment cmt"><p>:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Slice this matrix excluding the given row and column.</p></div><dl class="paramcmts block"><dt class="param">row</dt><dd class="cmt"><p>the row to exclude</p></dd><dt class="param">col</dt><dd class="cmt"><p>the column to exclude
</p></dd></dl><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="scalation.math.MatrixN" class="extype" href="">MatrixN</a> → <a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a></dd></dl></div>
    </li><li visbl="pub" name="scalation.math.MatrixN#solve" data-isabs="false">
      <a id="solve(VectorN[T])(Fractional[T]):VectorN[T]"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">solve</span>
        
        <span class="params">(<span name="b">b: <a name="scalation.math.VectorN" class="extype" href="VectorN.html">VectorN</a>[T]</span>)</span><span class="params">(<span class="implicit">implicit </span><span name="fr">fr: Fractional[T]</span>)</span><span class="result">: <a name="scalation.math.VectorN" class="extype" href="VectorN.html">VectorN</a>[T]</span>
      </span>
      </h4>
      <p class="shortcomment cmt">:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Solve for x in the equation a*x = b where a is this matrix (see lud above).</p><div class="fullcomment"><div class="comment cmt"><p>:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Solve for x in the equation a*x = b where a is this matrix (see lud above).</p></div><dl class="paramcmts block"><dt class="param">b</dt><dd class="cmt"><p>the constant vector.
</p></dd></dl><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="scalation.math.MatrixN" class="extype" href="">MatrixN</a> → <a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a></dd></dl></div>
    </li><li visbl="pub" name="scalation.math.MatrixN#solve" data-isabs="false">
      <a id="solve((Matrix[T], Matrix[T]),VectorN[T])(Fractional[T]):VectorN[T]"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">solve</span>
        
        <span class="params">(<span name="lu">lu: (<a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a>[T], <a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a>[T])</span>, <span name="b">b: <a name="scalation.math.VectorN" class="extype" href="VectorN.html">VectorN</a>[T]</span>)</span><span class="params">(<span class="implicit">implicit </span><span name="fr">fr: Fractional[T]</span>)</span><span class="result">: <a name="scalation.math.VectorN" class="extype" href="VectorN.html">VectorN</a>[T]</span>
      </span>
      </h4>
      <p class="shortcomment cmt">:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Solve for x in the equation l*u*x = b (see lud above).</p><div class="fullcomment"><div class="comment cmt"><p>:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Solve for x in the equation l*u*x = b (see lud above).</p></div><dl class="paramcmts block"><dt class="param">lu</dt><dd class="cmt"><p>the lower and upper triangular matrices</p></dd><dt class="param">b</dt><dd class="cmt"><p>the constant vector
</p></dd></dl><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="scalation.math.MatrixN" class="extype" href="">MatrixN</a> → <a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a></dd></dl></div>
    </li><li visbl="pub" name="scalation.math.MatrixN#solve" data-isabs="false">
      <a id="solve(Matrix[T],Matrix[T],VectorN[T])(Fractional[T]):VectorN[T]"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">solve</span>
        
        <span class="params">(<span name="l">l: <a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a>[T]</span>, <span name="u">u: <a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a>[T]</span>, <span name="b">b: <a name="scalation.math.VectorN" class="extype" href="VectorN.html">VectorN</a>[T]</span>)</span><span class="params">(<span class="implicit">implicit </span><span name="fr">fr: Fractional[T]</span>)</span><span class="result">: <a name="scalation.math.VectorN" class="extype" href="VectorN.html">VectorN</a>[T]</span>
      </span>
      </h4>
      <p class="shortcomment cmt">:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Solve for x in the equation l*u*x = b (see lud above).</p><div class="fullcomment"><div class="comment cmt"><p>:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Solve for x in the equation l*u*x = b (see lud above).</p></div><dl class="paramcmts block"><dt class="param">l</dt><dd class="cmt"><p>the lower triangular matrix</p></dd><dt class="param">u</dt><dd class="cmt"><p>the upper triangular matrix</p></dd><dt class="param">b</dt><dd class="cmt"><p>the constant vector
</p></dd></dl><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="scalation.math.MatrixN" class="extype" href="">MatrixN</a> → <a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a></dd></dl></div>
    </li><li visbl="pub" name="scalation.math.Matrix#sum" data-isabs="false">
      <a id="sum:T"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">sum</span>
        
        <span class="result">: T</span>
      </span>
      </h4>
      <p class="shortcomment cmt">Compute the sum of this matrix, i.</p><div class="fullcomment"><div class="comment cmt"><p>Compute the sum of this matrix, i.e., the sum of its elements.
</p></div><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a></dd></dl></div>
    </li><li visbl="pub" name="scalation.math.Matrix#sumLower" data-isabs="false">
      <a id="sumLower:T"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">sumLower</span>
        
        <span class="result">: T</span>
      </span>
      </h4>
      <p class="shortcomment cmt">Compute the sum of the lower triangular region of this matrix.</p><div class="fullcomment"><div class="comment cmt"><p>Compute the sum of the lower triangular region of this matrix.
</p></div><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a></dd></dl></div>
    </li><li visbl="pub" name="scala.AnyRef#synchronized" data-isabs="false">
      <a id="synchronized[T0](⇒ T0):T0"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">synchronized</span>
        <span class="tparams">[<span name="T0">T0</span>]</span>
        <span class="params">(<span name="arg0">arg0: ⇒ T0</span>)</span><span class="result">: T0</span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Attributes</dt><dd>final </dd><dt>Definition Classes</dt><dd>AnyRef</dd></dl></div>
    </li><li visbl="pub" name="scalation.math.MatrixN#t" data-isabs="false">
      <a id="t:MatrixN[T]"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">t</span>
        
        <span class="result">: <a name="scalation.math.MatrixN" class="extype" href="">MatrixN</a>[T]</span>
      </span>
      </h4>
      <p class="shortcomment cmt">:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Transpose this matrix (rows =&gt; columns).</p><div class="fullcomment"><div class="comment cmt"><p>:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Transpose this matrix (rows =&gt; columns).
</p></div><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="scalation.math.MatrixN" class="extype" href="">MatrixN</a> → <a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a></dd></dl></div>
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      <a id="toString():String"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">toString</span>
        
        <span class="params">()</span><span class="result">: String</span>
      </span>
      </h4>
      <p class="shortcomment cmt">:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Convert this matrix to a string.</p><div class="fullcomment"><div class="comment cmt"><p>:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Convert this matrix to a string.
</p></div><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="scalation.math.MatrixN" class="extype" href="">MatrixN</a> → AnyRef → Any</dd></dl></div>
    </li><li visbl="pub" name="scalation.math.Matrix#trace" data-isabs="false">
      <a id="trace:T"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">trace</span>
        
        <span class="result">: T</span>
      </span>
      </h4>
      <p class="shortcomment cmt">Compute the trace of this matrix, i.</p><div class="fullcomment"><div class="comment cmt"><p>Compute the trace of this matrix, i.e., the sum of the elements on the
 main diagonal.  Should also equal the sum of the eigenvalues.</p></div><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a></dd><dt>See also</dt><dd><span class="cmt"><p>Eigen.scala
</p></span></dd></dl></div>
    </li><li visbl="pub" name="scalation.math.MatrixN#update" data-isabs="false">
      <a id="update(Int,VectorN[T]):Unit"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">update</span>
        
        <span class="params">(<span name="i">i: <span name="scala.Int" class="extype">Int</span></span>, <span name="u">u: <a name="scalation.math.VectorN" class="extype" href="VectorN.html">VectorN</a>[T]</span>)</span><span class="result">: <span name="scala.Unit" class="extype">Unit</span></span>
      </span>
      </h4>
      <p class="shortcomment cmt">:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Set this matrix's row at the i-th index position to the vector u.</p><div class="fullcomment"><div class="comment cmt"><p>:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Set this matrix's row at the i-th index position to the vector u.</p></div><dl class="paramcmts block"><dt class="param">i</dt><dd class="cmt"><p>the row index</p></dd><dt class="param">u</dt><dd class="cmt"><p>the vector value to assign
</p></dd></dl><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="scalation.math.MatrixN" class="extype" href="">MatrixN</a> → <a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a></dd></dl></div>
    </li><li visbl="pub" name="scalation.math.MatrixN#update" data-isabs="false">
      <a id="update(Int,Int,T):Unit"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">update</span>
        
        <span class="params">(<span name="i">i: <span name="scala.Int" class="extype">Int</span></span>, <span name="j">j: <span name="scala.Int" class="extype">Int</span></span>, <span name="x">x: T</span>)</span><span class="result">: <span name="scala.Unit" class="extype">Unit</span></span>
      </span>
      </h4>
      <p class="shortcomment cmt">:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Set this matrix's element at the i,j-th index position to the scalar x.</p><div class="fullcomment"><div class="comment cmt"><p>:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Set this matrix's element at the i,j-th index position to the scalar x.</p></div><dl class="paramcmts block"><dt class="param">i</dt><dd class="cmt"><p>the row index</p></dd><dt class="param">j</dt><dd class="cmt"><p>the column index</p></dd><dt class="param">x</dt><dd class="cmt"><p>the scalar value to assign
</p></dd></dl><dl class="attributes block"> <dt>Definition Classes</dt><dd><a name="scalation.math.MatrixN" class="extype" href="">MatrixN</a> → <a name="scalation.math.Matrix" class="extype" href="Matrix.html">Matrix</a></dd></dl></div>
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      <a id="wait():Unit"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">wait</span>
        
        <span class="params">()</span><span class="result">: <span name="scala.Unit" class="extype">Unit</span></span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Attributes</dt><dd>final </dd><dt>Definition Classes</dt><dd>AnyRef</dd><dt>Annotations</dt><dd>
                <span class="name">@throws</span><span class="args">()</span>
              
        </dd></dl></div>
    </li><li visbl="pub" name="scala.AnyRef#wait" data-isabs="false">
      <a id="wait(Long,Int):Unit"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">wait</span>
        
        <span class="params">(<span name="arg0">arg0: <span name="scala.Long" class="extype">Long</span></span>, <span name="arg1">arg1: <span name="scala.Int" class="extype">Int</span></span>)</span><span class="result">: <span name="scala.Unit" class="extype">Unit</span></span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Attributes</dt><dd>final </dd><dt>Definition Classes</dt><dd>AnyRef</dd><dt>Annotations</dt><dd>
                <span class="name">@throws</span><span class="args">()</span>
              
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      <a id="wait(Long):Unit"></a>
      <h4 class="signature">
      <span class="kind">def</span>
      <span class="symbol"> 
        <span class="name">wait</span>
        
        <span class="params">(<span name="arg0">arg0: <span name="scala.Long" class="extype">Long</span></span>)</span><span class="result">: <span name="scala.Unit" class="extype">Unit</span></span>
      </span>
      </h4>
      <div class="fullcomment"><dl class="attributes block"> <dt>Attributes</dt><dd>final </dd><dt>Definition Classes</dt><dd>AnyRef</dd><dt>Annotations</dt><dd>
                <span class="name">@throws</span><span class="args">()</span>
              
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